I think that I can tell you the likely answers to your questions anyway!
Unless there's a VERY good reason (such as a student requiring urgent and intensive hospital treatment), no German university would be likely to allow a student to skip the Wintersemester and only to attend for the Sommersemester. Most university course are hierarchical, with the content of the Sommersemester relating back to the work that was done during the Wintersemester, so it might simply be impossible to jump in half way through the first year of the course. (It's also unlikely that any university faculty would be likely to put a candidate forward for the awarding of a degree if they've not studied for the entire duration of the course).
If you still want to ask the first of your three questions though, I suggest that you would need to include a (very good) REASON for making the request.
As the university will be receiving your coursework for any online studies by email, it's likely that they'll accept any necessary documentation to commence the course via the same means.
Your final question seems hardly worthy of consideration to me. If you're not going to be in a foreign country, you clearly don't need health insurance for being there! (However my draft email below covers the possibility of you being required to attend the university in person at some stage during the Wintersemester).
Moving on to the actual email though, although both Brits and American still tend to start snail-mailed letters with 'Dear' (as in 'Dear Mr Smith' or 'Dear Sir or Madam'), the practice is generally not used in emails. In most cases the sender simply launches straight into the main text of their message, although sometimes it's best to put an 'Fao' at the start of it. (e.g. 'Fao: Course admissions registrar).
So here's my amended version of your email. (I remind you that, unless you've got a very good REASON for seeking to skip the Wintersemester, it would probably be best to remove any reference to wishing to do so. However, for completeness, I've left that bit in for now. If you delete that paragraph, you can also delete the part I've placed within square brackets in the next paragraph too):
"Fao: Course Admissions Registrar.
I am looking forward to commencing my studies on the xxxxx course at yyyyy University in the new academic year.
I note that the Wintersemester's studies will be conducted online, with students not physically attending the university's campus until the commencement of the Sommersemester. As online study would be extremely difficult for me due to . . . REASON . . . , I wonder if it would be possible for me to delay the commencement of my studies until the start of the Sommersemester and then catch up on the missing work at a later date?
[If it is not possible for me to miss the online part of the course for the time being,] I assume that any coursework I will need to submit during the Wintersemester will be sent to my tutors by email. Can I do the same with any documentation that you might require prior to me commencing the course, such as examination certifates or proof of ID? (i.e. will scanned documents, sent by email, be acceptable or do I need to send my original documents to you via courier?)
As I will not be commencing face-to-face studies until next April, I plan to arrange my health insurance cover to start from that time. However if there will be any need for me to physically attend the campus prior to then, please let me know as soon as possible in order that I can amend my insurance cover accordingly.
I offer my thanks in advance of your anticipated response, which I look forward to receiving at your earliest convenience.
Kind regards
Fatema"